It is well known that NMR imaging methods utilize a combination of pulsed magnetic field gradients and pulsed RF magnetic fields to obtain NMR imaging information from nuclear spins situated in a selected region of an imaging sample. In several well-known methods, the pulsed RF magnetic fields involve multiple spin-echo RF pulse sequences. Most NMR methods employing multiple spin-echo pulse sequences utilize Carr-Purcell-Meiboom-Gill (CPMG) methods.
The CPMG methods involve the application of a 90.degree.:.tau.:180.degree.:2.tau.:180:2.tau.:180:2.tau.:180, etc., RF pulse sequence wherein the phase of the 180.degree. pulses is rotated by 90.degree. with respect to the phase of the 90.degree. pulse. Before the pulse sequence is applied, the nuclear magnets are at equilibrium such that they generate a net nuclear magnetization M aligned with the direction of an applied static field B.sub.o. For the purpose of explaining the effect of the RF pulse sequence on the nuclear magnetization M, the direction of the static field B.sub.o is typically chosen as the z-axis in a Cartesian coordinate system rotating at the Larmor frequency .omega..sub.o. Viewing the Cartesian coordinate system at the frequency .omega..sub.o so that the system appears stationary, the initiated 90.degree. pulse of the CPMG methods cause the magnetization M to rotate 90.degree. (hence the name "90.degree." pulse) into the x-y plane defined by the x and y axes of the Cartesian coordinate system. Subsequent application of the 180.degree. pulses causes the magnetization M to rotate through 180.degree. about the excitation axis.
In NMR imaging, magnetic field gradients are necessary to encode spatial information into the NMR signal. Because of these magnetic field gradients, the value of B.sub.o is not constant and therefore not all of the nuclear spins comprising the magnetization M have the same frequency.
Again considering the Cartesian coordinate system rotating at the Larmor frequency .omega..sub.o, the change in frequency caused by the spatial encoding of the magnetic field gradients causes the nuclear spins comprising the magnetization M to dephase after they have been rotated into the x-y plane by the 90.degree. RF pulse. By rotating the nuclear spins about a transverse axis in response to the application of a 180.degree. pulse, the dephasing effect is reversed and the nuclear spins pass through an in-phase position and then again begin to dephase. Application of subsequent 180.degree. pulses will cause the spins to again focus or become in-phase. Because of this rephasing characteristic, 180.degree. pulses used in spin-echo applications are often known as time reversal pulses.
When the spins focus in the x-y or transverse plane, an NMR signal can be detected by a receiver coil positioned to be sensitive along the transverse plane. The refocused magnetization M is commonly referred to as a "spin echo". Unfortunately, in the CPMG imaging methods where multiple spin-echo sequences are employed, the effects of imperfect 180.degree. pulses can be severe, and in practice the 180.degree. pulses are rarely ideal.
For the purpose of understanding its imaging effects, an imperfect 180.degree. pulse may be thought of as a composite of 0.degree., 90.degree. and 180.degree. pulses. Following the foregoing example, the 0.degree. pulse component will not rotate a group of nuclear spins and, of course, the 90.degree. pulse component rotates the spins 90.degree. in the Cartesian coordinate system. Just as each imperfect 180.degree. pulse may be thought of as a composite of 0.degree., 90.degree. and 180.degree. pulses, the magnetization M may be thought of as being comprised of groups of spins (isochromats) that are affected by the imperfect 180.degree. pulse as if the pulse is a composite of 0.degree., 90.degree. and 180.degree. pulses. Specifically, some groups of spins or isochromats may be considered to be affected by the imperfect 180.degree. pulse as if it were a perfect 180.degree. pulse. Other groups of spins may be affected as if the pulse was a 90.degree. pulse. And still other groups of spins may be affected as if the pulse was a 0.degree. pulse. Viewing the effect of the imperfect 180.degree. pulse in this manner, the ghosting artifacts generated by an imperfect 180.degree. pulse may be considered to be associated with 0.degree. and 90.degree. pulses.